On interactive anisotropic walks in two dimensions generated from a three state opinion dynamics model

TL;DR

This paper explores a two-dimensional anisotropic walk model driven by a three-state opinion dynamics system, revealing phase transitions and distinct distribution behaviors influenced by noise levels.

Contribution

It introduces a novel two-dimensional walk model based on a three-state opinion dynamics, analyzing its phase transition and distribution properties in a statistical physics context.

Findings

Three distinct regions identified as noise varies

Distribution transitions from non-conventional to Gaussian forms

Scaling laws exhibit power-law behavior and anisotropic features

Abstract

A system of interacting walkers is considered in a two-dimensional hypothetical space, where the dynamics of each walker are governed by the opinion states of the agents of a fully connected three-state opinion dynamics model. Such walks, studied in different models of statistical physics, are usually considered in one-dimensional virtual spaces. Here, the mapping is done in such a way that the walk is directed along the Y-axis while it can move either way along the X-axis. The walk shows that there are three distinct regions as the noise parameter, responsible for driving a continuous phase transition in the model, is varied. In absence of any noise, the scaling properties and the form of the distribution along either axis do not follow any conventional form. For any finite noise below the critical point the bivariate distribution of the displacements is found to be a modified biased Gaussian function while above it, only the marginal distribution along one direction is Gaussian. The marginal probability distributions can be extracted and the scaling forms of different quantities, showing power law behaviour, are obtained. The directed nature of the walk is reflected in the marginal distributions as well as in the exponents.